Adomian decomposition method for solving the Volterra integral form of the Lane–Emden equations with initial values and boundary conditions

摘要

In this paper, we use the systematic Adomian decomposition method to handle the integral form of the Lane–Emden equations with initial values and boundary conditions. The Volterra integral form of the Lane–Emden equation overcomes the singular behavior at the origin x=0. We confirm our belief that the Adomian decomposition method provides efficient algorithm for analytic approximate solutions of the equation. Our results are supported by investigating several numerical examples that include initial value problems and boundary value problems as well. Finally we consider the modified decomposition method of Rach, Adomian and Meyers for the Volterra integral form.